| This dissertation investigates two broad classes of nonlinear filtering: (1) Multilevel nonlinear filters for edge detection and noise suppression. (2) Enhancements of adaptive median filters.In the first category, we introduce two new classes of multilevel nonlinear filters for simultaneous edge detection and noise suppression, which we call a nested median filter/median averaging filter (NMF/MAF) pair and a a delayed decision filter/embedded median trimmed filter (DDF/EMTF) pair.Median filters and the median-related filters reported in the literature cause an edge shift in the presence of an impulse near the edge. The proposed filters in the first category reduce such edge shifting while suppressing impulsive as well as nonimpulsive noise.We show that at the noisy edge point the NMF and the DDF are substantially superior both theoretically and experimentally to the median filter, the We also show that in the noisy homogeneous region(non-edge point), the output bias errors of the MAF are zero and the output mean square error of the MAF are substantially close to those of the optimized single-level filters: the averager, the median filter, and the min-max filter under Gaussian, Laplacian, and uniform noise, respectively.Test results confirm that the NMF/MAF pair and the DDF/EMTF structure are each robust in preserving sharp edges, inhibiting edge shifting, and suppressing a wide variety of noise.The second broad class concerns enhancements of adaptive median filters. Based on two-types of image corrupted by impulse noise, we propose two new algorithms for adaptive median filters with variable window size for removal of impulses while preserving sharpness. The first one, called the ranked-order based adaptive median filter (RAMF), is based on a test for the presence of impulses in the center pixel itself followed by the test for the presence of residual impulses in the median filter output. The second one, called the impulse size based adaptive median filter (SAMF), is based on the detection of the size of the impulsive noise.It is shown that the RAMF is superior to the nonlinear mean... |
